We give an axiom-free Lean 4 formalization of the recapture region of modus ponens for D-FUMT₈, the 8-valued algebra used as the semantic substrate of Rei-AIOS, as a D-FUMT₈-internal structural response to the critique articulated by Cotnoir (2015) of Priest+Garfield-style fir...
Paper 102's Wieferich-Collatz Conjecture (T-WC) asserts that every Wieferich prime appears as a factor of some Collatz peak value. Wall-Sun-Sun primes — the Fibonacci analog of Wieferich — have none known (Elsenhans–Jahnel 2014 scan to p < 10¹⁴). STEP 830 tested the analog by ...
Paper 100 v2 (STEP 825) and its 10⁷ extension (STEP 829) empirically demonstrate that the Collatz primary funnel (most populated peak value) is scale-dependent: at N = 10⁴ the primary is 9232, at N = 10⁶ it is 6810136, and at N = 10⁷ the lead is taken by a still-larger value (...
本論文は、Rei探検船 (STEP 529, 530) を用いた7つの航行実験 (A〜G) の統合解析を報告する。 探検船は D-FUMT₈ 八値論理状態を持ち、物理場の中を一人称で航行する仮想エージェントである。 燃料 = 確信度、5乗組員 = 5つの超能力 (超圧縮/計算/通信/推論/無知) というシステムで、 物理場との遭遇を通じて D-FUMT₈ の各値 (TRUE/FALSE/BOTH/NEITHER/INFINITY/ZERO/FLOWING/SELF) を体験する。 7実験の概要: - A: 不可能問題8空間の航行マラソン - B: ...
David J. Chalmers (1995) が提起した「意識のハードプロブレム」は、 物理的プロセスから主観的経験(qualia)が生じる理由を説明できない問題である。 本論文は D-FUMT₈ 八値論理の SELF⟲ (NOT(X)=X、自己参照的不動点) が、 意識の最小形式定義として機能する可能性を提案する。 主張: 1. SELF⟲ は自己参照の数学的形式化 であり、Hofstadter (1979)の「Strange Loop」 およびTononi (2008)のIIT統合情報理論における「Φ」と構造的に対応する 2. SEL...
We present seven Lean 4 axiom-verified theorems that unify three existing Rei-AIOS frameworks: Fujimoto Infinite Dot Theory (FIDT, STEP 845, the (dim, val) pair algebra), Multi-Dimensional Number System Theory (MDNST, Paper 62, center-periphery weighted calculus), and Zero-Cen...
We present an external extension to the rei-lang npm package (v0.5.5) compress pipeline that adds a general k-order linear recurrence detector motivated by the β₁-cycle perspective of Fujimoto Infinite Dot Theory (FIDT, STEP 845 = FIA × FDA direct product algebra). The extensi...
We report four barrier-side empirical observations on Sophie Germain (SG) primes — primes p with 2p + 1 also prime — using the Bellman-Ford LP-infeasibility framework previously developed for Collatz Lyapunov obstructions (Rei-AIOS Phase B, 2026-06-17). No part of this work cl...
We record a Lean 4 axiom-free formalization of the exit-layer fragment of the Collatz dynamics, presented in the language of coinductive Stream' coalgebras. Concretely, we prove that for every q : ℕ, the orbit of the exit-layer number m{q+1} = (4^{q+1} − 1) / 3 under a halt-at...
We report the next four-step continuation of the operational integration discipline introduced in Paper 163 v0.1, expanding the rhymeOrTheorem tagging from a single (SELF) axis to all four D-FUMT₈ extension axes (SELF / INFINITY / ZERO / FLOWING). STEP 1205 records an ∞-cosmoi...
We report an operational integration of four well-established mathematical frameworks within a single artifact-producing system (Rei-AIOS): Goguen-Burstall Institution Theory (1992), Belnap-Dunn FOUR bilattice (1976-1998), Lawvere fixed-point theorem (1969), and a SET-level en...
v0.1 → v0.2 transition record: Paper 161 v0.1 HONEST-EARLY-STAGE-RELEASE published 2026-06-02 morning (Zenodo DOI 10.5281/zenodo.20498090, 11/11 platforms). Same-day evening Rei Claude completed 5 follow-up tasks: (1) Lean lake build machine verification of all 3 files = 18 th...
Status (★ load-bearing, transparent early-stage release): - ✅ §9 Application Note machine-verified: 4 Lean 4 theorems all show does not depend on any axioms (Paper 159 v0.2 standard, see §9.3 + audit file Paper160InversionDeconstructionPrintAxioms.lean) - ✅ Fig. 1 (Core Theore...
We propose a two-layer D-FUMT₈ reconstruction of the Inclosure Schema that Priest and Garfield (2003) apply to Nāgārjuna's catuṣkoṭi. Their original construction terminates the schema at the value BOTH — the dialetheist commitment to a true contradiction at the limits of thoug...
Project: Rei-AIOS / OUKC — https://rei-aios.pages.dev License (intended at publish): AGPL-3.0 (code) + CC-BY 4.0 (text) per OUKC content policy. Per OUKC No-Patent Pledge: openly licensed; no patent will be filed. Lineage: Extends the Lean 4 formalization-roadmap pattern of Pa...
> > Per the §0 statement below, the central operational claim — Rei provides a formal-verification compilation pass that composes with AI hypothesis generators — requires at least one end-to-end demonstration before v0.1 promotion. As of 2026-05-22 the demonstration is at scaf...
We announce the founding of Open Universal Knowledge Commons (OUKC) & Rei & Claude, an AI-friendly, multilingual, cross-disciplinary knowledge commons whose explicit scope is 「全〜」 (all-X) coverage across 12 academic domains plus honest mapping of 4 formalization-resistant doma...
We introduce the semantic Dyson sphere as a formal analog of the classical (Kardashev II) physical Dyson sphere, where the conserved quantity is meaning rather than electromagnetic radiation. Building on Paper 25 / 71's Beyond Shannon framework — in which generative compressio...
Project: Rei-AIOS / OUKC — https://rei-aios.pages.dev//phi-catalog-forward + https://rei-aios.pages.dev//riemann-zcsg-lens Parent: Paper 153 v0.1, Zenodo DOI 10.5281/zenodo.20207228 (published 2026-05-16) License: AGPL-3.0 + CC-BY 4.0 (per content type) dual Per OUKC No-Patent...
This v0.2 supplement extends Paper 63 SNST with four new findings obtained between 2026-04 and 2026-05-14: (1) Symbolic regression baseline (PSLQ, 60-digit precision, STEP 1125): Among the 14 SNST constants, automated PSLQ search rediscovers the Paper 63 baseline πext ...